英文标题：
《On time scaling of semivariance in a jump-diffusion process》
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作者：
Rodrigue Oeuvray and Pascal Junod
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最新提交年份：
2013
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英文摘要：
The aim of this paper is to examine the time scaling of the semivariance when returns are modeled by various types of jump-diffusion processes, including stochastic volatility models with jumps in returns and in volatility. In particular, we derive an exact formula for the semivariance when the volatility is kept constant, explaining how it should be scaled when considering a lower frequency. We also provide and justify the use of a generalization of the Ball-Torous approximation of a jump-diffusion process, this new model appearing to deliver a more accurate estimation of the downside risk. We use Markov Chain Monte Carlo (MCMC) methods to fit our stochastic volatility model. For the tests, we apply our methodology to a highly skewed set of returns based on the Barclays US High Yield Index, where we compare different time scalings for the semivariance. Our work shows that the square root of the time horizon seems to be a poor approximation in the context of semivariance and that our methodology based on jump-diffusion processes gives much better results.
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中文摘要：
本文的目的是研究当收益率由各种类型的跳跃-扩散过程建模时，半方差的时间标度，包括收益率和波动率跳跃的随机波动率模型。特别是，当波动率保持不变时，我们推导出了半方差的精确公式，解释了在考虑较低频率时，应如何对其进行缩放。我们还提供并证明了跳跃-扩散过程的球-环近似的推广，这种新模型似乎提供了更准确的下行风险估计。我们使用马尔可夫链蒙特卡罗（MCMC）方法来拟合我们的随机波动率模型。在测试中，我们将我们的方法应用于基于巴克莱美国高收益率指数的一组高度倾斜的收益率，其中我们比较了半方差的不同时间标度。我们的工作表明，在半方差的情况下，时间范围的平方根似乎不是一个很好的近似值，我们基于跳扩散过程的方法给出了更好的结果。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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